Chisquared target models

Swerling models were introduced by Peter Swerling and are used to describe the statistical properties of the radar crosssection of complex objects.
Contents
General Target Model
Swerling target models give the RCS of a given object using a distribution in the locationscale family of the chisquared distribution.
where σ_{av} refers to the mean value of σ. This is not always easy to determine, as certain objects may be viewed the most frequently from a limited range of angles. For instance, a seabased radar system is most likely to view a ship from the side, the front, and the back, but never the top or the bottom. m is the degree of freedom divided by 2. The degree of freedom used in the chisquared probability density function is a positive number related to the target model. Values of m between 0.3 and 2 have been found to closely approximate certain simple shapes, such as cylinders or cylinders with fins.
Since the ratio of the standard deviation to the mean value of the chisquared pdf is equal to m^{1/2}, larger values of m will result in less fluctuations. If m equals infinity, the target's RCS is nonfluctuating.
Swerling Target Models
Swerling target models are special cases of the ChiSquared target models with specific degrees of freedom. There are five different Swerling models, numbered I through V:
Swerling I
A model where the RCS varies according to a Chisquared probability density function with two degrees of freedom (m = 1). This applies to a target that is made up of many independent scatterers of roughly equal areas. As little as half a dozen scattering surfaces can produce this distribution. Swerling I describes a target whose radar crosssection is constant throughout a single scan, but varies independently from scan to scan. In this case, the pdf reduces to
Swerling I has been shown to be a good approximation when determining the RCS of objects in aviation.
Swerling II
Similar to Swerling I, except the RCS values returned are independent from pulse to pulse, instead of scan to scan.
Swerling III
A model where the RCS varies according to a Chisquared probability density function with four degrees of freedom (m = 2). This PDF approximates an object with one large scattering surface with several other small scattering surfaces. The RCS is constant through a single scan just as in Swerling I. The pdf becomes
Swerling IV
Similar to Swerling III, but the RCS varies from pulse to pulse rather than from scan to scan.
Swerling V (Also known as Swerling 0)
Constant RCS ().
References
 Skolnik, M. Introduction to Radar Systems: Third Edition. McGrawHill, New York, 2001.
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